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Help me to know how much was lost in a shift

In a convenience store, at the end of a shift, actual money must equal required money. In a particular shift, there was an overage of $10. The overage was not due to counting mistake but a cashier failed to key in a sale. He just opened the drawer, and put the money, $10. The coming shift took over with this overage of $10. At the end of the second shift, there was a shortage of $60. Assuming that there was no counting mistake with the actual money, how much money was lost during the second shift?

In a convenience store, at the end of a shift, actual money must equal required money. In a particular shift, there was an overage of $10. The overage was not due to counting mistake but a cashier failed to key in a sale. He just opened the drawer, and put the money, $10. The coming shift took over with this overage of $10. At the end of the second shift, there was a shortage of $60. Assuming that there was no counting mistake with the actual money, how much money was lost during the second shift?

What are your thoughts?

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My thoughts. According to me, the second shift lost $70. Since they started a shift with over $10, they shorted the $10, then shorted the $60. Is like a number line where we move from from +10 to -60. I tried to explain that to my colleagues they don't understand, they say the shift lost $50. That's they subtract 10 from 60. What do u think am I right or wrong?

Doesn't this depend on how a shortage is calculated/defined at the end of a shift?

Let me put forward some ludicrously small numbers as an example to try to think through it. Let's say that at the beginning of shift 1, there is no float, i.e. we start with $0 in the register (unrealistic, but a simplification). Let's say that the computer in the register claims that we made $100 in sales in shift 1. Let's say that at the end of shift 1, we count the money in the register, and our count comes up to $110. Okay, we conclude we have a $10 overage because a cashier failed to key in a $10 sale.

Let's say that shift 2 now happens, and at the end of it, the computer claims that we made an additional $200 in sales during shift 2.

I can think of two possible scenarios for what happens next. The two scenarios are two different ways for evaluating how much money we think we should have:

Scenario 1: the register-recorded sales for the two shifts are added up to determine the total quantity of money we should have in the register:

So we add $100 from shift 1 to $200 from shift 2, and we start with the "expectation" that we should have $300 in the register. We count up the total money in the register, and it comes up short by $60, i.e. we get a count of $240. At this point, because we are astute, we make a correction to the expected amount. We know it's not actually $300, but $310, because we started with a $10 surplus at the end of the first shift. So we conclude that the actual amount we are short by is:

$310 - $240 = $70

Scenario 2: the register-recorded sales for shift 2 are added to the actual float from shift 1 to determine the total quantity of money we should have in the register:

If this is the case, we started with the counted/verified $110 amount from shift 1, and added to it the computer-claimed amount of $200 additional sales from shift 2, coming up with an expected value in the register of $310. If we counted the money in the register and came up $60 short, that means we came up with a count of $250, and we really are $60 short.

So the answer for how much money was lost is either $70 or $60. Either way, your coworkers are wrong. It's definitely not $50.

Doesn't this depend on how a shortage is calculated/defined at the end of a shift?

Let me put forward some ludicrously small numbers as an example to try to think through it. Let's say that at the beginning of shift 1, there is no float, i.e. we start with $0 in the register (unrealistic, but a simplification). Let's say that the computer in the register claims that we made $100 in sales in shift 1. Let's say that at the end of shift 1, we count the money in the register, and our count comes up to $110. Okay, we conclude we have a $10 overage because a cashier failed to key in a $10 sale.

Let's say that shift 2 now happens, and at the end of it, the computer claims that we made an additional $200 in sales during shift 2.

I can think of two possible scenarios for what happens next. The two scenarios are two different ways for evaluating how much money we think we should have:

Scenario 1: the register-recorded sales for the two shifts are added up to determine the total quantity of money we should have in the register:

So we add $100 from shift 1 to $200 from shift 2, and we start with the "expectation" that we should have $300 in the register. We count up the total money in the register, and it comes up short by $60, i.e. we get a count of $240. At this point, because we are astute, we make a correction to the expected amount. We know it's not actually $300, but $310, because we started with a $10 surplus at the end of the first shift. So we conclude that the actual amount we are short by is:

$310 - $240 = $70

Scenario 2: the register-recorded sales for shift 2 are added to the actual float from shift 1 to determine the total quantity of money we should have in the register:

If this is the case, we started with the counted/verified $110 amount from shift 1, and added to it the computer-claimed amount of $200 additional sales from shift 2, coming up with an expected value in the register of $310. If we counted the money in the register and came up $60 short, that means we came up with a count of $250, and we really are $60 short.

So the answer for how much money was lost is either $70 or $60. Either way, your coworkers are wrong. It's definitely not $50.

U are awesome! Both answers are correct. It's either $70 or $60. Without no float, if we hand over a shift with all the money we have from the previous shift, with the overage and they come up with a shortage, then the answer will be $70. This is ur scenario 1. With float, the answer is 60. This is the correct answer as per the way we calculate shortage/overage at end of shift as u posed. This is scenario 2, and this is the one we use at my workplace. We reset the float to $200. If there is overage, it's not added to the float, it's taken away along with other monies in excess of $200 and dropped in a safe drop. The coming shift starts their shift with $200, regardless whether there was a shortage or overage with the previous shift. So if indeed there is a shortage in second shift of $60, then that's the actual shortage lost during that shift becoz the $10 overage from the previous shift wasn't included in the float they took over from the previous shift.

U are awesome! Both answers are correct. It's either $70 or $60. Without no float, if we hand over a shift with all the money we have from the previous shift, with the overage and they come up with a shortage, then the answer will be $70. This is ur scenario 1. With float, the answer is 60. This is the correct answer as per the way we calculate shortage/overage at end of shift as u posed. This is scenario 2, and this is the one we use at my workplace. We reset the float to $200. If there is overage, it's not added to the float, it's taken away along with other monies in excess of $200 and dropped in a safe drop. The coming shift starts their shift with $200, regardless whether there was a shortage or overage with the previous shift. So if indeed there is a shortage in second shift of $60, then that's the actual shortage lost during that shift becoz the $10 overage from the previous shift wasn't included in the float they took over from the previous shift.